SLOWING DOWN THE MOTION

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SLOWING DOWN THE MOTION
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SLOWING DOWN THE MOTION
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BALL ON TWO RAMPS
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GALILEOS ACCELERATION EXPERIMENT
From Two New Sciences p 178 A piece of wooden
moulding or scantling about 12 cubits long(!),
half a cubit wide, and three finger-breadths
thick was taken on its edge was cut a channel a
little more than one finger in breadth having
made this groove very straight, smooth, and
polished, and having lined it with parchment,
also as smooth and polished as possible, we
rolled along it a hard, smooth, and very round
bronze ball. Having placed this board in a
sloping position by raising one end above the
other we rolled the ball along the channel noting
the time required to make the descent. We then
rolled the ball only one-quarter of the length of
the channel, and found it precisely one-half of
the former. Next we tried other distances, and
always found the spaces traversed were to each
other as the squares of the times.
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GALILEO HI TECH
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DIRECT MEASUREMENMT OF g
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MARBLE IN SHOE BOX
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NON-ZERO INITIAL SPEED
v
v0
t
x vAVt ½(v0 v)t
v v0 at
x ½(v0 v0 at)t v0t 1/2at2
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EXAMPLE THROW ROCK UP
Choose upward to be positive displacement and
speed. (This choice is arbitrary)
Then v v0 -gt
Let v0 5m/s and g 10m/s2
When does the rock get to the top of its motion?
v 0 5 10t so 5 10t and t 0.5s
How high did it go?
y v0t 1/2gt2 5(0.5) 5(0.5)2 2.5 1.25
1.25m
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QUESTION
For the rock just thrown, what was its
acceleration at the very top of its motion?

• 10 m/s2
• 5 m/s2
• 0 m/s2
• - 5 m/s2
• E. - 10 m/s2

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SAME QUESTION USING INCLINED PLANE
Cart on track with motion sensor.
Start it initially moving upwards. In this case,
with the sensor at the top of the track,
downwards will be positive in the graphs shown.
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DROP ROCK FROM TOP OF BUILDING
Here we extend our earlier equations by adding
an initial displacement
y y0 1/2gt2
Let y0 50m.
y 50 5t2
When does it hit? Answer when y 0
0 50 5t2 so 5t2 50 and t2 10 so t
3.2 s